From 0a3ee99cdb0dfa9b9202ced71ae5c277dc18b0f4 Mon Sep 17 00:00:00 2001
From: Fredrik Jansson <fredrik.jansson.se@gmail.com>
Date: Sun, 12 Apr 2020 11:46:00 +0200
Subject: [PATCH] Changed dimension name R to D Changed N::from_x to
 crate::convert

---
 src/linalg/exp.rs | 230 ++++++++++++++++++++++------------------------
 1 file changed, 111 insertions(+), 119 deletions(-)

diff --git a/src/linalg/exp.rs b/src/linalg/exp.rs
index 8822027b..f68cbe6c 100644
--- a/src/linalg/exp.rs
+++ b/src/linalg/exp.rs
@@ -6,25 +6,25 @@ use crate::{
         dimension::{DimMin, DimMinimum, DimName},
         DefaultAllocator,
     },
-    try_convert, ComplexField, MatrixN, RealField,
+    convert, try_convert, ComplexField, MatrixN, RealField,
 };
 
 // https://github.com/scipy/scipy/blob/c1372d8aa90a73d8a52f135529293ff4edb98fc8/scipy/sparse/linalg/matfuncs.py
-struct ExpmPadeHelper<N, R>
+struct ExpmPadeHelper<N, D>
 where
     N: RealField,
-    R: DimName + DimMin<R>,
-    DefaultAllocator: Allocator<N, R, R> + Allocator<(usize, usize), DimMinimum<R, R>>,
+    D: DimName + DimMin<D>,
+    DefaultAllocator: Allocator<N, D, D> + Allocator<(usize, usize), DimMinimum<D, D>>,
 {
     use_exact_norm: bool,
-    ident: MatrixN<N, R>,
+    ident: MatrixN<N, D>,
 
-    a: MatrixN<N, R>,
-    a2: Option<MatrixN<N, R>>,
-    a4: Option<MatrixN<N, R>>,
-    a6: Option<MatrixN<N, R>>,
-    a8: Option<MatrixN<N, R>>,
-    a10: Option<MatrixN<N, R>>,
+    a: MatrixN<N, D>,
+    a2: Option<MatrixN<N, D>>,
+    a4: Option<MatrixN<N, D>>,
+    a6: Option<MatrixN<N, D>>,
+    a8: Option<MatrixN<N, D>>,
+    a10: Option<MatrixN<N, D>>,
 
     d4_exact: Option<N>,
     d6_exact: Option<N>,
@@ -37,16 +37,16 @@ where
     d10_approx: Option<N>,
 }
 
-impl<N, R> ExpmPadeHelper<N, R>
+impl<N, D> ExpmPadeHelper<N, D>
 where
     N: RealField,
-    R: DimName + DimMin<R>,
-    DefaultAllocator: Allocator<N, R, R> + Allocator<(usize, usize), DimMinimum<R, R>>,
+    D: DimName + DimMin<D>,
+    DefaultAllocator: Allocator<N, D, D> + Allocator<(usize, usize), DimMinimum<D, D>>,
 {
-    fn new(a: MatrixN<N, R>, use_exact_norm: bool) -> Self {
+    fn new(a: MatrixN<N, D>, use_exact_norm: bool) -> Self {
         ExpmPadeHelper {
             use_exact_norm,
-            ident: MatrixN::<N, R>::identity(),
+            ident: MatrixN::<N, D>::identity(),
             a,
             a2: None,
             a4: None,
@@ -64,9 +64,9 @@ where
         }
     }
 
-    fn a2(&self) -> &MatrixN<N, R> {
+    fn a2(&self) -> &MatrixN<N, D> {
         if self.a2.is_none() {
-            let ap = &self.a2 as *const Option<MatrixN<N, R>> as *mut Option<MatrixN<N, R>>;
+            let ap = &self.a2 as *const Option<MatrixN<N, D>> as *mut Option<MatrixN<N, D>>;
             unsafe {
                 *ap = Some(&self.a * &self.a);
             }
@@ -74,9 +74,9 @@ where
         self.a2.as_ref().unwrap()
     }
 
-    fn a4(&self) -> &MatrixN<N, R> {
+    fn a4(&self) -> &MatrixN<N, D> {
         if self.a4.is_none() {
-            let ap = &self.a4 as *const Option<MatrixN<N, R>> as *mut Option<MatrixN<N, R>>;
+            let ap = &self.a4 as *const Option<MatrixN<N, D>> as *mut Option<MatrixN<N, D>>;
             let a2 = self.a2();
             unsafe {
                 *ap = Some(a2 * a2);
@@ -85,11 +85,11 @@ where
         self.a4.as_ref().unwrap()
     }
 
-    fn a6(&self) -> &MatrixN<N, R> {
+    fn a6(&self) -> &MatrixN<N, D> {
         if self.a6.is_none() {
             let a2 = self.a2();
             let a4 = self.a4();
-            let ap = &self.a6 as *const Option<MatrixN<N, R>> as *mut Option<MatrixN<N, R>>;
+            let ap = &self.a6 as *const Option<MatrixN<N, D>> as *mut Option<MatrixN<N, D>>;
             unsafe {
                 *ap = Some(a4 * a2);
             }
@@ -97,11 +97,11 @@ where
         self.a6.as_ref().unwrap()
     }
 
-    fn a8(&self) -> &MatrixN<N, R> {
+    fn a8(&self) -> &MatrixN<N, D> {
         if self.a8.is_none() {
             let a2 = self.a2();
             let a6 = self.a6();
-            let ap = &self.a8 as *const Option<MatrixN<N, R>> as *mut Option<MatrixN<N, R>>;
+            let ap = &self.a8 as *const Option<MatrixN<N, D>> as *mut Option<MatrixN<N, D>>;
             unsafe {
                 *ap = Some(a6 * a2);
             }
@@ -109,11 +109,11 @@ where
         self.a8.as_ref().unwrap()
     }
 
-    fn a10(&mut self) -> &MatrixN<N, R> {
+    fn a10(&mut self) -> &MatrixN<N, D> {
         if self.a10.is_none() {
             let a4 = self.a4();
             let a6 = self.a6();
-            let ap = &self.a10 as *const Option<MatrixN<N, R>> as *mut Option<MatrixN<N, R>>;
+            let ap = &self.a10 as *const Option<MatrixN<N, D>> as *mut Option<MatrixN<N, D>>;
             unsafe {
                 *ap = Some(a6 * a4);
             }
@@ -123,28 +123,28 @@ where
 
     fn d4_tight(&mut self) -> N {
         if self.d4_exact.is_none() {
-            self.d4_exact = Some(one_norm(self.a4()).powf(N::from_f64(0.25).unwrap()));
+            self.d4_exact = Some(one_norm(self.a4()).powf(convert(0.25)));
         }
         self.d4_exact.unwrap()
     }
 
     fn d6_tight(&mut self) -> N {
         if self.d6_exact.is_none() {
-            self.d6_exact = Some(one_norm(self.a6()).powf(N::from_f64(1.0 / 6.0).unwrap()));
+            self.d6_exact = Some(one_norm(self.a6()).powf(convert(1.0 / 6.0)));
         }
         self.d6_exact.unwrap()
     }
 
     fn d8_tight(&mut self) -> N {
         if self.d8_exact.is_none() {
-            self.d8_exact = Some(one_norm(self.a8()).powf(N::from_f64(1.0 / 8.0).unwrap()));
+            self.d8_exact = Some(one_norm(self.a8()).powf(convert(1.0 / 8.0)));
         }
         self.d8_exact.unwrap()
     }
 
     fn d10_tight(&mut self) -> N {
         if self.d10_exact.is_none() {
-            self.d10_exact = Some(one_norm(self.a10()).powf(N::from_f64(1.0 / 10.0).unwrap()));
+            self.d10_exact = Some(one_norm(self.a10()).powf(convert(1.0 / 10.0)));
         }
         self.d10_exact.unwrap()
     }
@@ -159,7 +159,7 @@ where
         }
 
         if self.d4_approx.is_none() {
-            self.d4_approx = Some(one_norm(self.a4()).powf(N::from_f64(0.25).unwrap()));
+            self.d4_approx = Some(one_norm(self.a4()).powf(convert(0.25)));
         }
 
         self.d4_approx.unwrap()
@@ -175,7 +175,7 @@ where
         }
 
         if self.d6_approx.is_none() {
-            self.d6_approx = Some(one_norm(self.a6()).powf(N::from_f64(1.0 / 6.0).unwrap()));
+            self.d6_approx = Some(one_norm(self.a6()).powf(convert(1.0 / 6.0)));
         }
 
         self.d6_approx.unwrap()
@@ -191,7 +191,7 @@ where
         }
 
         if self.d8_approx.is_none() {
-            self.d8_approx = Some(one_norm(self.a8()).powf(N::from_f64(1.0 / 8.0).unwrap()));
+            self.d8_approx = Some(one_norm(self.a8()).powf(convert(1.0 / 8.0)));
         }
 
         self.d8_approx.unwrap()
@@ -207,48 +207,43 @@ where
         }
 
         if self.d10_approx.is_none() {
-            self.d10_approx = Some(one_norm(self.a10()).powf(N::from_f64(1.0 / 10.0).unwrap()));
+            self.d10_approx = Some(one_norm(self.a10()).powf(convert(1.0 / 10.0)));
         }
 
         self.d10_approx.unwrap()
     }
 
-    fn pade3(&mut self) -> (MatrixN<N, R>, MatrixN<N, R>) {
-        let b = [
-            N::from_f64(120.0).unwrap(),
-            N::from_f64(60.0).unwrap(),
-            N::from_f64(12.0).unwrap(),
-            N::from_f64(1.0).unwrap(),
-        ];
+    fn pade3(&mut self) -> (MatrixN<N, D>, MatrixN<N, D>) {
+        let b: [N; 4] = [convert(120.0), convert(60.0), convert(12.0), convert(1.0)];
         let u = &self.a * (self.a2() * b[3] + &self.ident * b[1]);
         let v = self.a2() * b[2] + &self.ident * b[0];
         (u, v)
     }
 
-    fn pade5(&mut self) -> (MatrixN<N, R>, MatrixN<N, R>) {
-        let b = [
-            N::from_f64(30240.0).unwrap(),
-            N::from_f64(15120.0).unwrap(),
-            N::from_f64(3360.0).unwrap(),
-            N::from_f64(420.0).unwrap(),
-            N::from_f64(30.0).unwrap(),
-            N::from_f64(1.0).unwrap(),
+    fn pade5(&mut self) -> (MatrixN<N, D>, MatrixN<N, D>) {
+        let b: [N; 6] = [
+            convert(30240.0),
+            convert(15120.0),
+            convert(3360.0),
+            convert(420.0),
+            convert(30.0),
+            convert(1.0),
         ];
         let u = &self.a * (self.a4() * b[5] + self.a2() * b[3] + &self.ident * b[1]);
         let v = self.a4() * b[4] + self.a2() * b[2] + &self.ident * b[0];
         (u, v)
     }
 
-    fn pade7(&mut self) -> (MatrixN<N, R>, MatrixN<N, R>) {
-        let b = [
-            N::from_f64(17297280.0).unwrap(),
-            N::from_f64(8648640.0).unwrap(),
-            N::from_f64(1995840.0).unwrap(),
-            N::from_f64(277200.0).unwrap(),
-            N::from_f64(25200.0).unwrap(),
-            N::from_f64(1512.0).unwrap(),
-            N::from_f64(56.0).unwrap(),
-            N::from_f64(1.0).unwrap(),
+    fn pade7(&mut self) -> (MatrixN<N, D>, MatrixN<N, D>) {
+        let b: [N; 8] = [
+            convert(17297280.0),
+            convert(8648640.0),
+            convert(1995840.0),
+            convert(277200.0),
+            convert(25200.0),
+            convert(1512.0),
+            convert(56.0),
+            convert(1.0),
         ];
         let u =
             &self.a * (self.a6() * b[7] + self.a4() * b[5] + self.a2() * b[3] + &self.ident * b[1]);
@@ -256,18 +251,18 @@ where
         (u, v)
     }
 
-    fn pade9(&mut self) -> (MatrixN<N, R>, MatrixN<N, R>) {
-        let b = [
-            N::from_f64(17643225600.0).unwrap(),
-            N::from_f64(8821612800.0).unwrap(),
-            N::from_f64(2075673600.0).unwrap(),
-            N::from_f64(302702400.0).unwrap(),
-            N::from_f64(30270240.0).unwrap(),
-            N::from_f64(2162160.0).unwrap(),
-            N::from_f64(110880.0).unwrap(),
-            N::from_f64(3960.0).unwrap(),
-            N::from_f64(90.0).unwrap(),
-            N::from_f64(1.0).unwrap(),
+    fn pade9(&mut self) -> (MatrixN<N, D>, MatrixN<N, D>) {
+        let b: [N; 10] = [
+            convert(17643225600.0),
+            convert(8821612800.0),
+            convert(2075673600.0),
+            convert(302702400.0),
+            convert(30270240.0),
+            convert(2162160.0),
+            convert(110880.0),
+            convert(3960.0),
+            convert(90.0),
+            convert(1.0),
         ];
         let u = &self.a
             * (self.a8() * b[9]
@@ -283,29 +278,29 @@ where
         (u, v)
     }
 
-    fn pade13_scaled(&mut self, s: u64) -> (MatrixN<N, R>, MatrixN<N, R>) {
-        let b = [
-            N::from_f64(64764752532480000.0).unwrap(),
-            N::from_f64(32382376266240000.0).unwrap(),
-            N::from_f64(7771770303897600.0).unwrap(),
-            N::from_f64(1187353796428800.0).unwrap(),
-            N::from_f64(129060195264000.0).unwrap(),
-            N::from_f64(10559470521600.0).unwrap(),
-            N::from_f64(670442572800.0).unwrap(),
-            N::from_f64(33522128640.0).unwrap(),
-            N::from_f64(1323241920.0).unwrap(),
-            N::from_f64(40840800.0).unwrap(),
-            N::from_f64(960960.0).unwrap(),
-            N::from_f64(16380.0).unwrap(),
-            N::from_f64(182.0).unwrap(),
-            N::from_f64(1.0).unwrap(),
+    fn pade13_scaled(&mut self, s: u64) -> (MatrixN<N, D>, MatrixN<N, D>) {
+        let b: [N; 14] = [
+            convert(64764752532480000.0),
+            convert(32382376266240000.0),
+            convert(7771770303897600.0),
+            convert(1187353796428800.0),
+            convert(129060195264000.0),
+            convert(10559470521600.0),
+            convert(670442572800.0),
+            convert(33522128640.0),
+            convert(1323241920.0),
+            convert(40840800.0),
+            convert(960960.0),
+            convert(16380.0),
+            convert(182.0),
+            convert(1.0),
         ];
         let s = s as f64;
 
-        let mb = &self.a * N::from_f64(2.0.powf(-s)).unwrap();
-        let mb2 = self.a2() * N::from_f64(2.0.powf(-2.0 * s)).unwrap();
-        let mb4 = self.a4() * N::from_f64(2.0.powf(-4.0 * s)).unwrap();
-        let mb6 = self.a6() * N::from_f64(2.0.powf(-6.0 * s)).unwrap();
+        let mb = &self.a * convert::<f64, N>(2.0_f64.powf(-s));
+        let mb2 = self.a2() * convert::<f64, N>(2.0_f64.powf(-2.0 * s));
+        let mb4 = self.a4() * convert::<f64, N>(2.0.powf(-4.0 * s));
+        let mb6 = self.a6() * convert::<f64, N>(2.0.powf(-6.0 * s));
 
         let u2 = &mb6 * (&mb6 * b[13] + &mb4 * b[11] + &mb2 * b[9]);
         let u = &mb * (&u2 + &mb6 * b[7] + &mb4 * b[5] + &mb2 * b[3] + &self.ident * b[1]);
@@ -323,13 +318,13 @@ fn factorial(n: u128) -> u128 {
 }
 
 /// Compute the 1-norm of a non-negative integer power of a non-negative matrix.
-fn onenorm_matrix_power_nonm<N, R>(a: &MatrixN<N, R>, p: u64) -> N
+fn onenorm_matrix_power_nonm<N, D>(a: &MatrixN<N, D>, p: u64) -> N
 where
     N: RealField,
-    R: DimName,
-    DefaultAllocator: Allocator<N, R, R> + Allocator<N, R>,
+    D: DimName,
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
 {
-    let mut v = crate::VectorN::<N, R>::repeat(N::from_f64(1.0).unwrap());
+    let mut v = crate::VectorN::<N, D>::repeat(convert(1.0));
     let m = a.transpose();
 
     for _ in 0..p {
@@ -339,11 +334,11 @@ where
     v.max()
 }
 
-fn ell<N, R>(a: &MatrixN<N, R>, m: u64) -> u64
+fn ell<N, D>(a: &MatrixN<N, D>, m: u64) -> u64
 where
     N: RealField,
-    R: DimName,
-    DefaultAllocator: Allocator<N, R, R> + Allocator<N, R>,
+    D: DimName,
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
 {
     // 2m choose m = (2m)!/(m! * (2m-m)!)
 
@@ -357,10 +352,10 @@ where
         factorial(2 * m as u128) / (factorial(m as u128) * factorial(2 * m as u128 - m as u128));
     let abs_c_recip = choose_2m_m * factorial(2 * m as u128 + 1);
     let alpha = a_abs_onenorm / one_norm(a);
-    let alpha = alpha / N::from_u128(abs_c_recip).unwrap();
+    let alpha: f64 = try_convert(alpha).unwrap() / abs_c_recip as f64;
 
-    let u = N::from_f64(2_f64.powf(-53.0)).unwrap();
-    let log2_alpha_div_u = try_convert((alpha / u).log2()).unwrap();
+    let u = 2_f64.powf(-53.0);
+    let log2_alpha_div_u = (alpha / u).log2();
     let value = (log2_alpha_div_u / (2.0 * m as f64)).ceil();
     if value > 0.0 {
         value as u64
@@ -369,11 +364,11 @@ where
     }
 }
 
-fn solve_p_q<N, R>(u: MatrixN<N, R>, v: MatrixN<N, R>) -> MatrixN<N, R>
+fn solve_p_q<N, D>(u: MatrixN<N, D>, v: MatrixN<N, D>) -> MatrixN<N, D>
 where
     N: ComplexField,
-    R: DimMin<R, Output = R> + DimName,
-    DefaultAllocator: Allocator<N, R, R> + Allocator<(usize, usize), DimMinimum<R, R>>,
+    D: DimMin<D, Output = D> + DimName,
+    DefaultAllocator: Allocator<N, D, D> + Allocator<(usize, usize), DimMinimum<D, D>>,
 {
     let p = &u + &v;
     let q = &v - &u;
@@ -381,11 +376,11 @@ where
     q.lu().solve(&p).unwrap()
 }
 
-fn one_norm<N, R>(m: &MatrixN<N, R>) -> N
+fn one_norm<N, D>(m: &MatrixN<N, D>) -> N
 where
     N: RealField,
-    R: DimName,
-    DefaultAllocator: Allocator<N, R, R>,
+    D: DimName,
+    DefaultAllocator: Allocator<N, D, D>,
 {
     let mut col_sums = vec![N::zero(); m.ncols()];
     for i in 0..m.ncols() {
@@ -399,11 +394,11 @@ where
     max
 }
 
-impl<N: RealField, R> MatrixN<N, R>
+impl<N: RealField, D> MatrixN<N, D>
 where
-    R: DimMin<R, Output = R> + DimName,
+    D: DimMin<D, Output = D> + DimName,
     DefaultAllocator:
-        Allocator<N, R, R> + Allocator<(usize, usize), DimMinimum<R, R>> + Allocator<N, R>,
+        Allocator<N, D, D> + Allocator<(usize, usize), DimMinimum<D, D>> + Allocator<N, D>,
 {
     /// Computes exponential of this matrix
     pub fn exp(&self) -> Self {
@@ -415,30 +410,30 @@ where
         let mut h = ExpmPadeHelper::new(self.clone(), true);
 
         let eta_1 = N::max(h.d4_loose(), h.d6_loose());
-        if eta_1 < N::from_f64(1.495585217958292e-002).unwrap() && ell(&h.a, 3) == 0 {
+        if eta_1 < convert(1.495585217958292e-002) && ell(&h.a, 3) == 0 {
             let (u, v) = h.pade3();
             return solve_p_q(u, v);
         }
 
         let eta_2 = N::max(h.d4_tight(), h.d6_loose());
-        if eta_2 < N::from_f64(2.539398330063230e-001).unwrap() && ell(&h.a, 5) == 0 {
+        if eta_2 < convert(2.539398330063230e-001) && ell(&h.a, 5) == 0 {
             let (u, v) = h.pade5();
             return solve_p_q(u, v);
         }
 
         let eta_3 = N::max(h.d6_tight(), h.d8_loose());
-        if eta_3 < N::from_f64(9.504178996162932e-001).unwrap() && ell(&h.a, 7) == 0 {
+        if eta_3 < convert(9.504178996162932e-001) && ell(&h.a, 7) == 0 {
             let (u, v) = h.pade7();
             return solve_p_q(u, v);
         }
-        if eta_3 < N::from_f64(2.097847961257068e+000).unwrap() && ell(&h.a, 9) == 0 {
+        if eta_3 < convert(2.097847961257068e+000) && ell(&h.a, 9) == 0 {
             let (u, v) = h.pade9();
             return solve_p_q(u, v);
         }
 
         let eta_4 = N::max(h.d8_loose(), h.d10_loose());
         let eta_5 = N::min(eta_3, eta_4);
-        let theta_13 = N::from_f64(4.25).unwrap();
+        let theta_13 = convert(4.25);
 
         let mut s = if eta_5 == N::zero() {
             0
@@ -452,10 +447,7 @@ where
             }
         };
 
-        s += ell(
-            &(&h.a * N::from_f64(2.0_f64.powf(-(s as f64))).unwrap()),
-            13,
-        );
+        s += ell(&(&h.a * convert::<f64, N>(2.0_f64.powf(-(s as f64)))), 13);
 
         let (u, v) = h.pade13_scaled(s);
         let mut x = solve_p_q(u, v);